Fishtank Learning

4th Grade Math
Unit 4: Fraction Equivalence and Ordering
Lesson 9

Objective

Recognize and generate equivalent fractions with larger units using visual models.

Anchor Tasks - Problem 1

a. What fraction of the rectangle below is shaded?

b. Laura says that $${{1\over4}}$$ of the model is shaded. Do you think she is correct? Explain why or why not by using the picture.

Guiding Questions

How is this rectangle different from ones we may have seen in Lessons 5–8?
What fraction of the rectangle is shaded? How do you know?
Is it true that $${{{{1\over4}}}}$$ of it is shaded? How do you know?
(Display a similar rectangle where all of the shaded pieces fill the top row instead of being spread out.) Which rectangle is more shaded? How do you know they are equal? How does this rectangle more clearly demonstrate that $${{{{1\over4}}}}$$ of it is shaded?
What do you notice about the relationship between the number of units and the size of those units in $$\frac{3}{12}$$ and $$\frac{1}{4}$$?
(Draw a rectangle that is either much smaller or larger than the original one above, shading $${{3\over{12}}}$$ of it.) Are the shaded portions still equal? Why?

Anchor Tasks - Problem 2

A point is shown on the number line diagram below.

Write three equivalent fractions that name this point.

Guiding Questions

What fraction is represented on the number line diagram?
How can you use the number line to create larger units? How can you use those larger units to find fractions that are equivalent to $${{8\over12}}$$?
How is the process for finding equivalent fractions with larger units similar to and different from the process for finding equivalent fractions with smaller units?

Notes

Two examples of number lines that model equivalent fractions are shown below.

Anchor Tasks - Problem 3

Solve for the missing value.

a. $${{8\over24}={\square\over6}}$$

b. $${{32\over10}={16\over\square}}$$

Guiding Questions

What can you draw to help you find the missing value?
What can we draw to represent $$\frac{20}{24}$$? How can we group that model to represent sixths? How many sixths do we have?
What can we draw to represent $$\frac{32}{10}$$? How can we group that model to represent sixteen units? How many units do we have?

Notes

Note that if students use an area model to help them solve, it may require rearranging some shaded fractional units in order to be able to group them to find the equivalent fraction. For example, if students represent $$\frac{20}{24}$$ like this:

They can rearrange the shaded pieces like so:

Making it easy to group to show sixths, five of which are shaded:

Problem Set

View Problem Set

Discussion of Problem Set

Look at #2c. What denominator made this statement true? Is there another way to rename this fraction? (Discuss how this is equivalent to the whole number 2.)
How did you shade the fraction strip in #3? What made this pair of equivalent fractions different from many of the others we’ve looked at so far? Because of that difference, how could you ensure that they were equivalent?
Look at #4. I think the correct answer is C. Do you agree or disagree? Why? What error did I make?

Target Task - Problem 1

The model below represents one whole.

Which fraction is equivalent to the one represented by the shaded part of the model?

A. $${{1\over8}}$$

B. $${{1\over4}}$$

C. $${{1\over3}}$$

D. $${{4\over3}}$$

Target Task - Problem 2

A point is shown on the number line diagram below.

Write three equivalent fractions for the location of this point.

Target Task - Problem 3

Use the number line to explain how you know the fractions in #2 are equivalent.

Word Problem

Alison has a mug that holds 8 ounces of coffee. Alison also has a SuperJug that holds 40 ounces of coffee. How many times more coffee does the SuperJug hold compared to the mug?

Fishtank Learning

4th Grade MathUnit 4: Fraction Equivalence and OrderingLesson 9

Objective

Anchor Tasks - Problem 1

Anchor Tasks - Problem 2

Anchor Tasks - Problem 3

Problem Set

Target Task - Problem 1

Target Task - Problem 2

Target Task - Problem 3

Word Problem

4th Grade Math
Unit 4: Fraction Equivalence and Ordering
Lesson 9